{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 对用户进行聚类\n",
    "\n",
    "数据来源于Kaggle竞赛：Event Recommendation Engine Challenge，根据\n",
    "events they’ve responded to in the past\n",
    "user demographic information\n",
    "what events they’ve seen and clicked on in our app\n",
    "用户对某个事件是否感兴趣\n",
    "\n",
    "竞赛官网：\n",
    "https://www.kaggle.com/c/event-recommendation-engine-challenge/data\n",
    "\n",
    "由于用户众多（3w+），可以对用户进行聚类\n",
    "事件描述信息在users.csv文件：共110维特征\n",
    "user_id\n",
    "locale：地区，语言\n",
    "birthyear：出身年\n",
    "gender：性别\n",
    "joinedAt：用户加入APP的时间，ISO-8601 UTC time\n",
    "location：地点\n",
    "timezone：时区\n",
    "\n",
    "作业要求：\n",
    "根据用户的属性进行聚类（KMeans聚类）\n",
    "尝试K=20， 40， 80，并计算各自CH_scores。\n",
    "\n",
    "提示：由于样本数目较多，建议使用MiniBatchKMeans。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. 特征工程：20分\n",
    "2. 聚类：30分\n",
    "3. CH_Score计算：30分\n",
    "4. 画图：10分\n",
    "5. 保存结果到文件：10分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#导入必要的工具包\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.cluster import MiniBatchKMeans\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import metrics\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "import time\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. 特征工程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>locale</th>\n",
       "      <th>birthyear</th>\n",
       "      <th>gender</th>\n",
       "      <th>joinedAt</th>\n",
       "      <th>location</th>\n",
       "      <th>timezone</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3197468391</td>\n",
       "      <td>id_ID</td>\n",
       "      <td>1993</td>\n",
       "      <td>male</td>\n",
       "      <td>2012-10-02T06:40:55.524Z</td>\n",
       "      <td>Medan  Indonesia</td>\n",
       "      <td>480.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3537982273</td>\n",
       "      <td>id_ID</td>\n",
       "      <td>1992</td>\n",
       "      <td>male</td>\n",
       "      <td>2012-09-29T18:03:12.111Z</td>\n",
       "      <td>Medan  Indonesia</td>\n",
       "      <td>420.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>823183725</td>\n",
       "      <td>en_US</td>\n",
       "      <td>1975</td>\n",
       "      <td>male</td>\n",
       "      <td>2012-10-06T03:14:07.149Z</td>\n",
       "      <td>Stratford  Ontario</td>\n",
       "      <td>-240.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1872223848</td>\n",
       "      <td>en_US</td>\n",
       "      <td>1991</td>\n",
       "      <td>female</td>\n",
       "      <td>2012-11-04T08:59:43.783Z</td>\n",
       "      <td>Tehran  Iran</td>\n",
       "      <td>210.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3429017717</td>\n",
       "      <td>id_ID</td>\n",
       "      <td>1995</td>\n",
       "      <td>female</td>\n",
       "      <td>2012-09-10T16:06:53.132Z</td>\n",
       "      <td>NaN</td>\n",
       "      <td>420.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      user_id locale birthyear  gender                  joinedAt  \\\n",
       "0  3197468391  id_ID      1993    male  2012-10-02T06:40:55.524Z   \n",
       "1  3537982273  id_ID      1992    male  2012-09-29T18:03:12.111Z   \n",
       "2   823183725  en_US      1975    male  2012-10-06T03:14:07.149Z   \n",
       "3  1872223848  en_US      1991  female  2012-11-04T08:59:43.783Z   \n",
       "4  3429017717  id_ID      1995  female  2012-09-10T16:06:53.132Z   \n",
       "\n",
       "             location  timezone  \n",
       "0    Medan  Indonesia     480.0  \n",
       "1    Medan  Indonesia     420.0  \n",
       "2  Stratford  Ontario    -240.0  \n",
       "3        Tehran  Iran     210.0  \n",
       "4                 NaN     420.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#读取数据\n",
    "df = pd.read_csv(\"users.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38209"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_records = df.shape[0]\n",
    "n_records"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 38209 entries, 0 to 38208\n",
      "Data columns (total 7 columns):\n",
      "user_id      38209 non-null int64\n",
      "locale       38209 non-null object\n",
      "birthyear    38209 non-null object\n",
      "gender       38100 non-null object\n",
      "joinedAt     38152 non-null object\n",
      "location     32745 non-null object\n",
      "timezone     37773 non-null float64\n",
      "dtypes: float64(1), int64(1), object(5)\n",
      "memory usage: 2.0+ MB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#并统计有多少不同的users（n_users）\n",
    "def get_uniqueUsers():\n",
    "    uniqueUsers = set()\n",
    "    \n",
    "    for i in range(n_records):\n",
    "        uniqueUsers.add(df.loc[i,'user_id'])\n",
    "    \n",
    "    n_events = len(uniqueUsers)\n",
    "    return n_events\n",
    "\n",
    "n_users = get_uniqueUsers()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38209"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_users"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 所有的user都相互独立，user_id不作为聚类属性, 所以把改列去除\n",
    "#### 同时，location的缺失值比较到，也进行去除"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>locale</th>\n",
       "      <th>birthyear</th>\n",
       "      <th>gender</th>\n",
       "      <th>joinedAt</th>\n",
       "      <th>timezone</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>id_ID</td>\n",
       "      <td>1993</td>\n",
       "      <td>male</td>\n",
       "      <td>2012-10-02T06:40:55.524Z</td>\n",
       "      <td>480.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>id_ID</td>\n",
       "      <td>1992</td>\n",
       "      <td>male</td>\n",
       "      <td>2012-09-29T18:03:12.111Z</td>\n",
       "      <td>420.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>en_US</td>\n",
       "      <td>1975</td>\n",
       "      <td>male</td>\n",
       "      <td>2012-10-06T03:14:07.149Z</td>\n",
       "      <td>-240.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>en_US</td>\n",
       "      <td>1991</td>\n",
       "      <td>female</td>\n",
       "      <td>2012-11-04T08:59:43.783Z</td>\n",
       "      <td>210.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>id_ID</td>\n",
       "      <td>1995</td>\n",
       "      <td>female</td>\n",
       "      <td>2012-09-10T16:06:53.132Z</td>\n",
       "      <td>420.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  locale birthyear  gender                  joinedAt  timezone\n",
       "0  id_ID      1993    male  2012-10-02T06:40:55.524Z     480.0\n",
       "1  id_ID      1992    male  2012-09-29T18:03:12.111Z     420.0\n",
       "2  en_US      1975    male  2012-10-06T03:14:07.149Z    -240.0\n",
       "3  en_US      1991  female  2012-11-04T08:59:43.783Z     210.0\n",
       "4  id_ID      1995  female  2012-09-10T16:06:53.132Z     420.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#user_id不作为聚类属性\n",
    "df = df.drop([\"user_id\"], axis=1)\n",
    "        \n",
    "#location有缺失值，粗暴抛弃\n",
    "#也可以将缺失值作为另外一类：others\n",
    "df = df.drop([\"location\"], axis=1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#特征编码\n",
    "import datetime\n",
    "import hashlib\n",
    "import locale\n",
    "\n",
    "from collections import defaultdict\n",
    "from sklearn.preprocessing import normalize\n",
    "\n",
    "class FeatureEng:\n",
    "    def __init__(self):\n",
    "         # 载入 locales，初始化为 0\n",
    "        self.localeIdMap = defaultdict(int)\n",
    "        #得到所有可用的locale的键值\n",
    "        for i, l in enumerate(locale.locale_alias.keys()):\n",
    "          self.localeIdMap[l] = i + 1\n",
    "        \n",
    "        # 载入 gender id 字典\n",
    "        ##缺失补0\n",
    "        self.genderIdMap = defaultdict(int, {'NaN': 0, \"male\":1, \"female\":2})\n",
    "\n",
    "  \n",
    "    def getLocaleId(self, locstr):\n",
    "        #字母小写\n",
    "        return self.localeIdMap[locstr.lower()]\n",
    "\n",
    "    def getGenderId(self, genderStr):\n",
    "        return self.genderIdMap[genderStr]\n",
    "\n",
    "    def getJoinedYearMonth(self, dateString):\n",
    "        try:\n",
    "            dttm = datetime.datetime.strptime(dateString, \"%Y-%m-%dT%H:%M:%S.%fZ\")\n",
    "            #return \"\".join([str(dttm.year), str(dttm.month)])\n",
    "            return (dttm.year-2010)*12 + dttm.month\n",
    "        except:  #缺失补0\n",
    "          return 0\n",
    "\n",
    "    def getBirthYearInt(self, birthYear):\n",
    "        #缺失补0\n",
    "        try:\n",
    "          return 0 if birthYear == \"None\" else int(birthYear)\n",
    "        except:\n",
    "          return 0\n",
    "\n",
    "    def getTimezoneInt(self, timezone):\n",
    "        try:\n",
    "          return int(timezone)\n",
    "        except:  #缺失值处理\n",
    "          return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "FE = FeatureEng()\n",
    "\n",
    "cols = ['LocaleId', 'BirthYearInt', 'GenderId', 'JoinedYearMonth', 'TimezoneInt']\n",
    "n_cols = len(cols)\n",
    "userMatrix = np.zeros((df.shape[0],n_cols), dtype=np.int)\n",
    "\n",
    "for i in range(df.shape[0]): \n",
    "    userMatrix[i, 0] = FE.getLocaleId(df.loc[i,'locale'])\n",
    "    userMatrix[i, 1] = FE.getBirthYearInt(df.loc[i,'birthyear'])\n",
    "    userMatrix[i, 2] = FE.getGenderId(df.loc[i,'gender'])\n",
    "    userMatrix[i, 3] = FE.getJoinedYearMonth(df.loc[i,'joinedAt'])\n",
    "    #userMatrix[i, 4] = FE.getCountryId(df[''])\n",
    "    userMatrix[i, 4] = FE.getTimezoneInt(df.loc[i,'timezone'])\n",
    "\n",
    "# 归一化用户矩阵\n",
    "userMatrix = normalize(userMatrix, norm=\"l1\", axis=0, copy=False)\n",
    "\n",
    "df_FE = pd.DataFrame(data=userMatrix, columns=cols)  \n",
    "#mmwrite(\"US_userMatrix\", userMatrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LocaleId</th>\n",
       "      <th>BirthYearInt</th>\n",
       "      <th>GenderId</th>\n",
       "      <th>JoinedYearMonth</th>\n",
       "      <th>TimezoneInt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000036</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000019</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>0.000036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000036</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000019</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>0.000031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000020</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000019</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>-0.000018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000020</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000038</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000036</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000038</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>0.000031</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   LocaleId  BirthYearInt  GenderId  JoinedYearMonth  TimezoneInt\n",
       "0  0.000036      0.000027  0.000019         0.000026     0.000036\n",
       "1  0.000036      0.000027  0.000019         0.000026     0.000031\n",
       "2  0.000020      0.000027  0.000019         0.000026    -0.000018\n",
       "3  0.000020      0.000027  0.000038         0.000027     0.000016\n",
       "4  0.000036      0.000027  0.000038         0.000026     0.000031"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_FE.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 38209 entries, 0 to 38208\n",
      "Data columns (total 5 columns):\n",
      "LocaleId           38209 non-null float64\n",
      "BirthYearInt       38209 non-null float64\n",
      "GenderId           38209 non-null float64\n",
      "JoinedYearMonth    38209 non-null float64\n",
      "TimezoneInt        38209 non-null float64\n",
      "dtypes: float64(5)\n",
      "memory usage: 1.5 MB\n"
     ]
    }
   ],
   "source": [
    "#缺失值填补\n",
    "#BirthYearInt\n",
    "#JoinedYearMonth     38152 non-null object\n",
    "#TimezoneInt     37773 non-null float64\n",
    "#mean_BirthYearInt = np.mean(df_FE[\"BirthYearInt\"]) \n",
    "#df_FE.loc[df_FE[\"BirthYearInt\"] == 0, \"BirthYearInt\"] = mean_BirthYearInt\n",
    "df_FE.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MiniBatchKMeans(batch_size=100, compute_labels=True, init='k-means++',\n",
       "        init_size=None, max_iter=100, max_no_improvement=10,\n",
       "        n_clusters=100, n_init=3, random_state=None,\n",
       "        reassignment_ratio=0.01, tol=0.0, verbose=0)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import MiniBatchKMeans\n",
    "\n",
    "n_clusters = 100\n",
    "km = MiniBatchKMeans(n_clusters = n_clusters)\n",
    "km.fit(df_FE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#保存预测结果\n",
    "df_FE['cluster_100'] = km.predict(df_FE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_FE.to_csv('users_FE.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LocaleId</th>\n",
       "      <th>BirthYearInt</th>\n",
       "      <th>GenderId</th>\n",
       "      <th>JoinedYearMonth</th>\n",
       "      <th>TimezoneInt</th>\n",
       "      <th>cluster_100</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000036</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000019</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>0.000036</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000036</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000019</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>0.000031</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000020</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000019</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>-0.000018</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000020</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000038</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000036</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.000038</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>0.000031</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   LocaleId  BirthYearInt  GenderId  JoinedYearMonth  TimezoneInt  cluster_100\n",
       "0  0.000036      0.000027  0.000019         0.000026     0.000036           86\n",
       "1  0.000036      0.000027  0.000019         0.000026     0.000031           83\n",
       "2  0.000020      0.000027  0.000019         0.000026    -0.000018           10\n",
       "3  0.000020      0.000027  0.000038         0.000027     0.000016           14\n",
       "4  0.000036      0.000027  0.000038         0.000026     0.000031           77"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_FE.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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